Frequency hopping sequence using galois field

Abstract

Frequency hopping enables a plurality of channels to share the same bandwidth without interference. The present invention utilizes Galois Field theory to define frequency hopping sequences for a plurality of channels which share the same bandwidth.

We claim: 
     
       1. A frequency-hopping communication method for enabling up to p-1 channels of a plurality of channels, channel (1), channel (2), . . . , channel (p-1), where p is a prime number, to share a same frequency band, comprising the step of: for each channel, changing carrier frequency on which data is one of modulated and demodulated every m th  fixed length time interval, to an m th  frequency of a unique predetermined sequence of carrier frequencies assigned to said channel (n), where n=1 . . . (p-1), formed from p frequencies f(0), f(1), f(2), . . . , f(p-1) selected from said frequency band but the order of the frequencies for each channel being different, and wherein said m th  frequency in the sequence for channel (n) is given by f(m*n) where m*n indicates multiplication in a Galois field GF(p) and 0≦m≦p-1.   
     
     
       2. The method of claim 1 wherein said frequency band is 902-928 MHz and p=61. 
     
     
       3. The method of claim 1 wherein said frequency band is 2400-2483.5 MHz and p=79. 
     
     
       4. The method of claim 1, wherein each of said sequences from m=0 to m=p-1 defines a super frame, wherein said frequency f(0) is assigned to all channels at time m=0, said method further comprising the steps of: at a master, modulating onto carrier frequency f(0) a channel identification for an n th  channel and a slave identification, at time m=0, and   at each slave, demodulating from said carrier frequency f(0) at least said slave identification, at time m=0 and, at said slave indicated by said slave identification, changing carrier frequency to f(1*n) at time m=1.